Powers & roots

Here is a card from a game.

Write down the number from the card that is a multiple of 5

Write down the number from the card that is a factor of 40

Write down the number from the card that is a prime number.

Write down the number from the card that is a square number.

c and d are consecutive cube numbers, where c 4.5³ d

Work out the value of d – c

The square of a whole number is a two-digit number.

Work out the smallest number that could have been squared and the largest number that could have been squared.

Which has the larger value 0.8² or 0.8³ ? Tick a box.

Give a reason for your answer.

Work out the value of 3³

Write 10 000 as a power of 10

Work out the value of 1.5²

Work out the value of 1.5²

Work out the value of 19²

Write down the value of 3²

Work out the value of 2⁴

Between which two consecutive integers does the square root of 210 lie?

Here are two calculations, A and B.

Use approximations to show that answer to A answer to B

A code has five different digits written in order, starting with the smallest. The last digit is the only square number. The middle digit is the only even number.

Work out the code.

Write down the value of 2³

Work out 3.45 + 2.07 – 1.3

A fair coin is thrown a number of times. The probability that every throw results in Heads is How many times is the coin thrown?

The first two cube numbers are 1 and 8

Show that the 3rd cube number can be written as the sum of three different prime numbers.

The first two cube numbers are 1 and 8

Show that the 3rd cube number can be written as the sum of three different prime numbers.

Here is a list of numbers. 14 9 20 29 3 45 33

Which number in the list is a multiple of 4 ?

Which number in the list is a square number?

Which two numbers in the list have a total of 43 ?

Work out largest number in the list ÷ smallest number in the list

Work out (– 4) × (– 3)

Work out 6 × (– 5)

Work out (–8)²

Work out 10³

Work out the value of a. You must show your working.

Give your answer as a mixed number.

Circle the possible value of x.

1.9 20 45 290

Complete the boxes using two different even numbers and two different odd numbers.

Complete the boxes using a factor of 12 and

Complete the boxes using a square number and a prime number.

Circle the value of 3² + 4²

14 17 25 49

Write a number in the box to make the calculation correct.

Write a number in the box to make the calculation correct.

Write a fraction in the box to make the calculation correct.

Write the same number in both boxes to make the calculation correct.

Complete this statement.

k is a whole number between 40 and 50 The cube root of k is 3, to the nearest whole number. Work out the largest possible value of k.

Fay tries to solve x² = 100 She says, ‘‘The only possible value of x is 10’’ Give a reason why she is not correct.

Give your answer as a decimal.

Give your answer in standard form.

k is a whole number between 40 and 50 The cube root of k is 3, to the nearest whole number. Work out the largest possible value of k.

Fay tries to solve x² = 100 She says, ‘‘The only possible value of x is 10’’ Give a reason why she is not correct.

Write down the two prime numbers between 25 and 35

Write down one cube number between 100 and 300

1 2^x = 32 Circle the value of x.

4 5 6 7

Here are two solid cubes, X and Y. The mass of X is 10.976 kg The area of each face of X is 784 cm²

Zayan wants to know the density of Y. He assumes that Y is identical to X.

What density should he get for Y? Give your answer in grams per cubic centimetre.

In fact, the mass of Y is less than the mass of X the area of each face of Y is greater than the area of each face of X.

What does this mean about the actual density of Y? Tick one box.

Show that 2125 can be written as a cube number multiplied by a prime number between 10 and 20

Calculate 2⁷ × 5²

The square root of x is 4 Circle the value of x²

256 2 16 8

m² 9 Circle the possible value of m.

Which one of these is a square number and a cube number? Circle your answer.

100 1000 10 000 1 000 000

c = 2 10 × 3 × 5 6 Work out 18 c. Give your answer as a product of prime factors in index form.

Give your answer as an integer.

Write down the value of 7 0

Work out the value of 32

Write down an even whole number that is also a square number.

Write down all the cube numbers between 100 and 400

Write down two numbers that are multiples of 3 and multiply to make 216

Circle the value of 5 3

8 15 25 125

Which of these numbers is three less than a square number? Circle your answer.

5 19 22 34

Which two numbers, when added together, make a cube number? Circle your answer.

1 and 8 2 and 4 9 and 18 8 and 64

Work out cube root of 512: reciprocal of 0.4 Give your answer in the form n: 1

Circle the number that is one less than a cube number.

20 22 24 26

Solve x² = 196

Work out the value of a.

Work out the value of a.

Circle the cube number.

9 10 000 333 729

What is 625 as a power of 5 ? Circle your answer.

Work out the value of 3⁶ –

The solution of 3^x = 300 lies between two consecutive integers. Work out the two integers.

n is an odd number. p is a prime number. In each part write down possible values of n and p so that

n + p is a square number.

np is a square number.

Which of these numbers is half of a square number? Circle your answer.

1 2 3 4

Circle the cube number.

100 1000 10 000 100 000

Show that 268 can be written as the sum of a power of 3 and a square number.

Show that 268 can be written as the sum of a power of 3 and a square number.

Work out 12 as an improper fraction.

10 25 32 64

Show that there are exactly five 3-digit cube numbers.